If the sample size is multiplied by 4, what happens to the standard deviation of the distribution of sample means?

Increasing the sample size by a factor of 4 or multiplying it by 4 is equal to increasing the standard error by 1/2.  Therefore, the interval will be half as varied.  This also works almost for population averages as lengthy as the multiplier from the t-curve doesn't modify much when increasing the sample size.

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times both sides by 2, times () by 8, add alile terms, move terms, add alike and caculate divide both sides by 3